{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Discretizers\n",
    "\n",
    "This package supports discretization methods and mapping functions.\n",
    "\n",
    "## Installation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "Pkg.add(\"Discretizers\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Once the installation is complete you can use it anywhere by running"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "using Discretizers"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Discretization\n",
    "\n",
    "### Categorical Labels\n",
    "\n",
    "You can construct an object for mapping labels to integer indeces"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "data = [:cat, :dog, :dog, :cat, :cat, :elephant]\n",
    "catdisc = CategoricalDiscretizer(data);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The resulting object can be used to encode your source labels to their categorical labels"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      ":cat becomes: 1\n",
      ":dog becomes: 2\n",
      "data becomes: [1,2,2,1,1,3]\n"
     ]
    }
   ],
   "source": [
    "println(\":cat becomes: \", encode(catdisc, :cat))\n",
    "println(\":dog becomes: \", encode(catdisc, :dog))\n",
    "println(\"data becomes: \", encode(catdisc, data))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can also transform back"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 becomes: cat\n",
      "2 becomes: dog\n",
      "[1,2,3] becomes: [:cat,:dog,:elephant]\n"
     ]
    }
   ],
   "source": [
    "println(\"1 becomes: \", decode(catdisc, 1))\n",
    "println(\"2 becomes: \", decode(catdisc, 2))\n",
    "println(\"[1,2,3] becomes: \", decode(catdisc, [1,2,3]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "The CategoricalDiscretizer works with any object type"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "CategoricalDiscretizer([\"A\", \"B\", \"C\"])\n",
    "CategoricalDiscretizer([5000, 1200, 100])\n",
    "CategoricalDiscretizer([:dog, \"hello world\", NaN]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Linear Discretization\n",
    "\n",
    "Linear discretization into a series of bins is supported as well\n",
    "\n",
    "Here we construct a linear discretizer that maps $[0,0.5) \\rightarrow 1$ and $[0.5,1] \\rightarrow 2$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "bin_edges = [0.0,0.5,1.0]\n",
    "lindisc = LinearDiscretizer(bin_edges);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Encoding works the same way"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.2 becomes: 1\n",
      "0.7 becomes: 2\n",
      "0.5 becomes: 2\n",
      "it works on arrays: [1,2,1]\n"
     ]
    }
   ],
   "source": [
    "println(\"0.2 becomes: \", encode(lindisc, 0.2))\n",
    "println(\"0.7 becomes: \", encode(lindisc, 0.7))\n",
    "println(\"0.5 becomes: \", encode(lindisc, 0.5))\n",
    "println(\"it works on arrays: \", encode(lindisc, [0.0,0.8,0.2]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Decoding is a bit different. Here we obtain the bin and sample from it uniformally"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 becomes: 0.1887493587068908\n",
      "2 becomes: 0.5460050358882282\n",
      "it works on arrays: [0.8104340883570698,0.454060686695556,0.9457654175718269]\n"
     ]
    }
   ],
   "source": [
    "println(\"1 becomes: \", decode(lindisc, 1))\n",
    "println(\"2 becomes: \", decode(lindisc, 2))\n",
    "println(\"it works on arrays: \", decode(lindisc, [2,1,2]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Some other functions are supported"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "number of labels: 3  2\n",
      "bin centers:      [0.25,0.75]\n",
      "extrama of a bin: (0.5,1.0)\n"
     ]
    }
   ],
   "source": [
    "println(\"number of labels: \", nlabels(catdisc), \"  \", nlabels(lindisc))\n",
    "println(\"bin centers:      \", bincenters(lindisc))\n",
    "println(\"extrama of a bin: \", extrema(lindisc, 2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Both discretizers can be constructed to map to other integer types"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0x01"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "catdisc = CategoricalDiscretizer(data, Int32)\n",
    "lindisc = LinearDiscretizer(bin_edges, UInt8)\n",
    "encode(lindisc, 0.2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Discretization Algorithms\n",
    "\n",
    "In many cases one would like to determine the bin edges for a Linear Discretizer automatically from data. This package supports several algorithms to do just that."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Uniform Width\n",
    "  \n",
    "  `DiscretizeUniformWidth(nbins)` - divide the domain evenly into `nbins`\n",
    "  \n",
    "* Uniform Count\n",
    "\n",
    "  `DiscretizeUniformCount(nbins)` - divide the domain into `nbins` where each bin has approximately equal count\n",
    "  \n",
    "* Bayesian Blocks\n",
    "\n",
    "  `DiscretizeBayesianBlocks()` - determines an appropriate number of bins by maximizing a Bayesian prior.\n",
    "  See [this website](http://www.astroml.org/examples/algorithms/plot_bayesian_blocks.html) for an overview."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4-element Array{Float64,1}:\n",
       " -2.85658 \n",
       " -0.598978\n",
       "  1.65863 \n",
       "  3.91623 "
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nbins = 3\n",
    "data  = randn(1000)\n",
    "edges = binedges(DiscretizeUniformWidth(nbins), data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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      ],
      "text/plain": [
       "PGFPlots.GroupPlot([PGFPlots.Axis(PGFPlots.Plots.Plot[PGFPlots.Plots.Linear(2x17 Array{Real,2}:\n",
       " -14.8231  -14.8231  -12.8364  -10.8497  …  11.004    12.9907   14.9774\n",
       "   0.0      11.577    16.1071   33.2209      9.06025   7.04686   0.0   ,nothing,nothing,\"const plot, mark=none, fill=blue!60\",nothing,nothing)],\"Uniform Width\",\"x\",nothing,\"pdf(x)\",nothing,nothing,nothing,nothing,nothing,0,nothing,nothing,nothing,nothing,nothing,nothing,nothing,nothing,nothing,nothing,nothing,nothing,nothing,nothing,nothing,nothing),PGFPlots.Axis(PGFPlots.Plots.Plot[PGFPlots.Plots.Linear(2x17 Array{Real,2}:\n",
       " -14.8231  -14.8231   -6.60423   -5.19549  …    3.0474   4.67614  14.9774\n",
       "   0.0      35.0412  204.439    476.45        176.824   27.8607    0.0   ,nothing,nothing,\"const plot, mark=none, fill=blue!60\",nothing,nothing)],\"Uniform Count\",\"x\",nothing,\"pdf(x)\",nothing,nothing,nothing,nothing,nothing,0,nothing,nothing,nothing,nothing,nothing,nothing,nothing,nothing,nothing,nothing,nothing,nothing,nothing,nothing,nothing,nothing),PGFPlots.Axis(PGFPlots.Plots.Plot[PGFPlots.Plots.Linear(2x21 Array{Real,2}:\n",
       " -14.8231  -14.8231  -9.90599  …   4.53939   5.85829  8.8699  14.9774\n",
       "   0.0      15.6596  41.1833      99.325    38.1856   9.3328   0.0   ,nothing,nothing,\"const plot, mark=none, fill=blue!60\",nothing,nothing)],\"Bayesian Blocks\",\"x\",nothing,\"pdf(x)\",nothing,nothing,nothing,nothing,nothing,0,nothing,nothing,nothing,nothing,nothing,nothing,nothing,nothing,nothing,nothing,nothing,nothing,nothing,nothing,nothing,nothing)],(3,1),nothing,\"horizontal sep = 1.75cm\")"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using PGFPlots\n",
    "using Distributions\n",
    "\n",
    "# draw a set of variables and\n",
    "# filter values to a reasonable range\n",
    "srand(0)\n",
    "data = [rand(Cauchy(-5, 1.8), 500);\n",
    "        rand(Cauchy(-4, 0.8), 2000);\n",
    "        rand(Cauchy(-1, 0.3), 500);\n",
    "        rand(Cauchy( 2, 0.8), 1000);\n",
    "        rand(Cauchy( 4, 1.5), 500)]\n",
    "data = filter!(x->-15.0 <= x <= 15.0, data)\n",
    "\n",
    "g = GroupPlot(3, 1, groupStyle = \"horizontal sep = 1.75cm\")\n",
    "\n",
    "discalgs = [(\"Uniform Width\", DiscretizeUniformWidth(15)),\n",
    "            (\"Uniform Count\", DiscretizeUniformCount(15)),\n",
    "            (\"Bayesian Blocks\", DiscretizeBayesianBlocks())]\n",
    "\n",
    "for (name, discalg) in discalgs\n",
    "    disc = LinearDiscretizer(binedges(discalg, data))\n",
    "    counts = get_discretization_counts(disc, data)    \n",
    "    arr_x, arr_y = get_histogram_plot_arrays(disc.binedges, counts ./ binwidths(disc))\n",
    "    push!(g, Axis(Plots.Linear(arr_x, convert(Vector{Float64}, arr_y), style=\"const plot, mark=none, fill=blue!60\"), \n",
    "          ymin=0, xlabel=\"x\", ylabel=\"pdf(x)\", title=name))\n",
    "end\n",
    "\n",
    "g"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Automatically Determine Number of Uniform-Width Bins\n",
    "\n",
    "Several algorithms exist for deterimining the number of uniform-width bins.\n",
    "Simply enter the algorithm as a symbol into `DiscretizeUniformWidth`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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      "text/plain": [
       "PGFPlots.GroupPlot([PGFPlots.Axis(PGFPlots.Plots.Plot[PGFPlots.Plots.Linear(2x68 Array{Real,2}:\n",
       " -14.8231  -14.8231   -14.3716  -13.9201  …  14.0743   14.5259   14.9774\n",
       "   0.0       6.64418   17.7178   11.0736      4.42945   6.64418   0.0   ,nothing,nothing,\"const plot, mark=none, fill=blue!60\",nothing,nothing)],\"sqrt\",nothing,nothing,nothing,nothing,nothing,nothing,nothing,nothing,0,nothing,nothing,nothing,nothing,nothing,nothing,nothing,nothing,nothing,nothing,nothing,nothing,nothing,nothing,nothing,nothing),PGFPlots.Axis(PGFPlots.Plots.Plot[PGFPlots.Plots.Linear(2x16 Array{Real,2}:\n",
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       "   0.0      12.6843   16.9125   36.6437      9.39581   7.04686   0.0   ,nothing,nothing,\"const plot, mark=none, fill=blue!60\",nothing,nothing)],\"sturges\",nothing,nothing,nothing,nothing,nothing,nothing,nothing,nothing,0,nothing,nothing,nothing,nothing,nothing,nothing,nothing,nothing,nothing,nothing,nothing,nothing,nothing,nothing,nothing,nothing),PGFPlots.Axis(PGFPlots.Plots.Plot[PGFPlots.Plots.Linear(2x35 Array{Real,2}:\n",
       " -14.8231  -14.8231  -13.9201  -13.017  …  13.1713   14.0743   14.9774\n",
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       "   0.0      11.4092   13.691      10.2683   9.12736   5.7046   0.0   ,nothing,nothing,\"const plot, mark=none, fill=blue!60\",nothing,nothing)],\"scott\",nothing,nothing,nothing,nothing,nothing,nothing,nothing,nothing,0,nothing,nothing,nothing,nothing,nothing,nothing,nothing,nothing,nothing,nothing,nothing,nothing,nothing,nothing,nothing,nothing),PGFPlots.Axis(PGFPlots.Plots.Plot[PGFPlots.Plots.Linear(2x43 Array{Real,2}:\n",
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       "   0.0      11.0065   13.7582   13.7582      8.25489   6.87908   0.0   ,nothing,nothing,\"const plot, mark=none, fill=blue!60\",nothing,nothing)],\"auto\",nothing,nothing,nothing,nothing,nothing,nothing,nothing,nothing,0,nothing,nothing,nothing,nothing,nothing,nothing,nothing,nothing,nothing,nothing,nothing,nothing,nothing,nothing,nothing,nothing)],(3,3),nothing,\"horizontal sep = 1.75cm, vertical sep = 1.5cm\")"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g = GroupPlot(3, 3, groupStyle = \"horizontal sep = 1.75cm, vertical sep = 1.5cm\")\n",
    "\n",
    "discalgs = [:sqrt, # used by Excel and others for its simplicity and speed\n",
    "            :sturges, # R's default method, only good for near-Gaussian data\n",
    "            :rice, # commonly overestimates the number of bins required\n",
    "            :doane, # improves Sturges’ for non-normal datasets.\n",
    "            :scott, # less robust estimator that that takes into account data variability and data size.\n",
    "            :fd, # Freedman Diaconis Estimator, robust\n",
    "            :auto, # max between :fd and :sturges. Good all-round performance\n",
    "            ]\n",
    "\n",
    "for discalg in discalgs\n",
    "    disc = LinearDiscretizer(binedges(DiscretizeUniformWidth(discalg), data))\n",
    "    counts = get_discretization_counts(disc, data)    \n",
    "    arr_x, arr_y = get_histogram_plot_arrays(disc.binedges, counts ./ binwidths(disc))\n",
    "    push!(g, Axis(Plots.Linear(arr_x, convert(Vector{Float64}, arr_y), style=\"const plot, mark=none, fill=blue!60\"), \n",
    "          ymin=0, title=string(discalg)))\n",
    "end\n",
    "\n",
    "g"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A third algorithm, MODL, was implemented to find optimal bins given both a continuous data set and a labelled discrete data set. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4-element Array{AbstractFloat,1}:\n",
       " -2.58175 \n",
       " -0.229589\n",
       "  1.87765 \n",
       "  2.6983  "
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = [randn(100); randn(100)+1.0]\n",
    "labels = [fill(:cat, 100); fill(:dog, 100)]\n",
    "integer_labels = encode(CategoricalDiscretizer([:cat, :dog]), labels)\n",
    "edges = binedges(DiscretizeMODL_Optimal(), data, integer_labels)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "More information on MODL can be found [here](http://nbviewer.ipython.org/github/sisl/Discretizers.jl/blob/master/doc/MODL/DiscretizationMODL.ipynb)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  }
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